Multipole Theory in Electromagnetism Classical, Quantum, and Symmetry Aspects, with Applications

by Raab, R. E.; de Lange, O. L.

• ISBN13: 9780198567271
• ISBN10: 0198567278
• Format: Hardcover
• Copyright: 2005-01-06
• Publisher: Oxford University Press

Summary

This book provides an introduction to the classical, quantum and symmetry aspects of multipole theory, demonstrating the successes of the theory and also its unphysical aspects. It presents a transformation theory, which removes these unphysical properties. The book will be of interest to physics students wishing to advance their knowledge of multipole theory, and also a useful reference work for molecular and optical physicists, theoretical chemists working on multipole effects, solid state physicists studying the effects of electromagnetic fields on condensed matter, engineers and applied mathematicians with interests in anisotrpoic materials. An interesting recent development has been the increasing use of computer calculations in applications of multipole theory. The book should assist computational physicists and chemists wishing to work in this area to acquire the necessary background in multipole theory.

Table of Contents

1 Classical multipole theory	1	(31)
1.1 Multipole expansion for the potential of a finite static charge distribution	1	(4)
1.2 Dependence of electric multipole moments on origin	5	(1)
1.3 Permanent and induced multipole moments	6	(1)
1.4 Force and torque in an external electrostatic field	7	(1)
1.5 Potential energy of a charge distribution in an electrostatic field	8	(2)
1.6 Multipole expansion for the vector potential of a finite distribution of steady current	10	(2)
1.7 Dependence of magnetic multipole moments on origin	12	(1)
1.8 Force and torque in an external magnetostatic field	13	(1)
1.9 Potential energy of a current distribution in a magnetostatic field	14	(1)
1.10 Multipole expansions for the dynamic scalar and vector potentials	15	(2)
1.11 The far-and near-zone limits	17	(1)
1.12 Macroscopic media	18	(5)
1.13 Maxwell's macroscopic equations: multipole forms for D and H	23	(2)
1.14 Discussion	25	(2)
1.15 Primitive moments versus traceless moments	27	(2)
1.15.1 A charge distribution	27	(1)
1.15.2 Macroscopic media	28	(1)
References	29	(3)
2 Quantum theory of multipole moments and polarizabilities	32	(27)
2.1 Semi-classical quantum mechanics	32	(1)
2.2 Electrostatic perturbation	33	(4)
2.3 Buckingham's derivation of electrostatic multipole moments	37	(1)
2.4 Magnetostatic perturbation	38	(2)
2.5 Time-dependent fields: standard gauge	40	(5)
2.6 Time-dependent fields: the Barron-Gray gauge	45	(2)
2.7 Polarizabilities for harmonic plane wave fields	47	(3)
2.8 Absorption of radiation	50	(1)
2.9 Additional static magnetic polarizabilities	51	(1)
2.10 Symmetries	52	(1)
2.11 Macroscopic multipole moment and polarizability densities	53	(1)
2.12 Phenomenology of the wave-matter interaction	54	(2)
References	56	(3)
3 Space and time properties	59	(25)
3.1 Coordinate transformations	59	(1)
3.2 Vectors	60	(2)
3.3 Cartesian tensors	62	(3)
3.4 Time reversal	65	(2)
3.5 The space and time nature of various tensors	67	(3)
3.6 Symmetry and property tensors	70	(5)
3.7 Origin dependence of polarizability tensors	75	(4)
3.8 A pictorial determination of symmetry conditions	79	(3)
3.9 Discussion	82	(1)
References	82	(2)
4 Linear constitutive relations from multipole theory	84	(16)
4.1 Constitutive relations	84	(2)
4.2 Origin independence	86	(1)
4.3 Symmetries	86	(4)
4.4 The "Post constraint"	90	(2)
4.5 Comparison with direct multipole results	92	(3)
4.5.1 Electric dipole order	92	(1)
4.5.2 Electric quadrupole-magnetic dipole order	93	(1)
4.5.3 Electric octopole-magnetic quadrupole order	94	(1)
4.6 Discussion	95	(3)
References	98	(2)
5 Transmission and scattering effects: direct multipole results	100	(45)
5.1 The wave equation	100	(3)
5.2 Intrinsic Faraday rotation in a ferromagnetic crystal	103	(3)
5.3 Natural optical activity	106	(4)
5.4 Time-odd linear birefringence in magnetic cubics	110	(1)
5.5 Optical properties in the Jones calculus	111	(1)
5.6 Gyrotropic birefringence	112	(3)
5.7 Linear birefringence in non-magnetic cubic crystals (Lorentz birefringence)	115	(3)
5.8 Intrinsic Faraday rotation in magnetic cubics	118	(2)
5.9 The Kerr effect in an ideal gas	120	(4)
5.10 Forward scattering theory of the Kerr effect	124	(3)
5.11 Birefringence induced in a gas by an electric field gradient: forward scattering theory	127	(9)
5.11.1 Forward scattering by a molecule	128	(1)
5.11.2 Induced moments	129	(1)
5.11.3 Forward scattering by a lamina	130	(1)
5.11.4 The electrostatic field	131	(1)
5.11.5 Radiated field for linearly polarized light	132	(1)
5.11.6 Field-gradient-induced birefringence	133	(2)
5.11.7 Comparison between theory and experiment	135	(1)
5.12 Birefringence induced in a gas by an electric field gradient: wave theory	136	(4)
5.13 Discussion	140	(1)
References	141	(4)
6 Reflection effects: direct multipole results	145	(27)
6.1 Reflection and the reflection matrix	145	(2)
6.2 The principle of reciprocity	147	(3)
6.3 Equations of continuity	150	(3)
6.4 Matching conditions in multipole theory	153	(3)
6.5 The reflection matrix for non-magnetic uniaxial and cubic crystals	156	(6)
6.6 Solutions of the wave equation	162	(3)
6.7 Reflection coefficients	165	(3)
6.8 Tests of translational and time-reversal invariance	168	(1)
6.9 Discussion	169	(1)
References	170	(2)
7 Transformations of the response fields and the constitutive tensor	172	(6)
7.1 Gauge transformations of the 4-vector potential	172	(1)
7.2 "Gauge transformations" of response fields	173	(1)
7.3 Faraday transformations	174	(1)
7.4 Transformations of linear constitutive relations in multipole theory	174	(3)
References	177	(1)
8 Applications of the gauge and Faraday transformations	178	(13)
8.1 Electric dipole order	178	(2)
8.2 Electric quadrupole-magnetic dipole order, non-magnetic medium	180	(3)
8.3 Electric quadrupole-magnetic dipole order, magnetic medium	183	(3)
8.4 Discussion	186	(3)
References	189	(2)
9 Transmission and reflection effects: transformed multipole results	191	(20)
9.1 The wave equation and transmission	191	(1)
9.2 Reflection from non-magnetic uniaxial and cubic crystals	192	(3)
9.3 Explicit results for non-magnetic uniaxial crystals	195	(2)
9.4 Explicit results for non-magnetic cubic crystals	197	(1)
9.5 Tests of translational and time-reversal invariance	198	(1)
9.6 Reflection from antiferromagnetic Cr2O3: first configuration	199	(3)
9.7 Reflection from antiferromagnetic Cr2O3: second configuration	202	(3)
9.8 Comparison with experiment for Cr2O3	205	(1)
9.9 Uniqueness of fields	206	(1)
9.10 Summary	206	(4)
References	210	(1)
A Transformations involving J	211	(2)
B Magnetostatic field	213	(1)
C Magnetostatic force	214	(1)
D Magnetostatic torque	215	(1)
E Integral transformations	216	(2)
F Origin dependence of a polarizability tensor	218	(2)
G Invariance of transformed tensors	220	(1)
Glossary of symbols	221	(8)
Index	229